Solute concentration measurements generally use the well-known Beer-Lambert law, which relates the solute molecular density and molecular absorption cross-section coefficient with the light intensity transmitted through a certain path length of solution. In the case of uniform solute density, the relation can be expressed as follows:I1=I0e−αcl  (1)where I0 is the light intensity entering the sampled solution, I1 is the light intensity exiting the sampled solution, α is the molecular absorption cross-section coefficient, c is the molecular density of the solute molecules in the measured sample (also referred to as the “number density” or the “concentration”), and l is the length of the light path traversed by the light beam in the measured sample.
If I1 is measured and I0, α, and l are known, the concentration c can be calculated using equation (1). For simplicity, the solvent is assumed to be transparent and any scattering effects of light caused by the solvent and/or solute molecules is assumed to be absent or negligible.
In laboratory instruments, the common practice used to measure an unknown concentration of a known solute in a fluid is to first measure the light transmittance, defined as the ratio I1/I0 from equation (1), through two measurement states using a light detector: a first measurement state, referred to as state A, in which the light is measured with no sample in the light path with the signal output of the light detector (referred to as the “reference measurement signal”) being proportional to I0; and a second measurement state, referred to as state B, in which the light is measured with the sample in the light path with the signal output of the light detector (referred to as the “sample measurement signal”) being proportional to I1. When using this methodology to measure the concentration, there is no need to accurately know the incoming light intensity I0, as the incoming light intensity will cancel out in the light transmittance ratio (I1/I0).
When measuring flowing liquid samples in-line, it is usually cumbersome and impractical to introduce and remove the fluid sample from the light path as in states B and A above. A more widely used alternative methodology relies on an optical switching method, which makes the light beam travel first through the fluid sample and then through a second light path that does not include the fluid sample. This optical switching method is easier to implement, since the switching between the sample and no-sample measurement is done optically, by controlling optical elements external to the liquid stream. The path of state A, above, may be a path through air or vacuum, a path through the same solvent without solute, or a solution made of the same solvent and an accurately known concentration of the same solute material or any other material of known transmittance. In this way, the signal output of light detector in states A and B are obtained, and their ratio, corrected to the known transmittance of the reference sample, being equal to I1/I0, can be used to obtain the concentration c from equation (1) above, or using a similar equation, by using the knowledge of a and path length l.
FIGS. 1A and 1B illustrate a schematic representation of a typical scheme for implementing such an optical switching method. A light source 12 generates a beam of light which is directed by a first lens 24a and passes through either a reference fluid (FIG. 1A-state A) or the fluid sample (FIG. 1B-state B). The light beam that exits the reference or fluid sample is passed through a second lens 24b before impinging on a light detector 14. In state A (FIG. 1A), a pair of switching mirrors 90a and 90b are moved, such that the light beam from the light source 12, directed by the first lens 24a, is reflected from the first switching mirror 90a, off of a first fixed mirror 92a, to pass through the reference fluid, where the light beam is then reflected from a second fixed mirror 92b, and off of the second switching mirror 90b through the second lens 24b and to the light detector 14. In state B (FIG. 1B), the pair of switching mirrors 90a and 90b are moved such that the light beam from the light source 12, directed by the first lens 24a, passes through fluid sample, where the light beam then passes through the second lens 24b onto the light detector 14. The dashed line 94 represents the light path traversed by the light beam in the states A and B. Note that in the implementation illustrated in FIGS. 1A and 1B, the first lens 24a may be omitted if the light source 12 generates a directional beam of light.
One drawback of such an optical switching method and other conceptually similar methods is that the switching mechanism uses different external optical components in two different optical paths. In the scheme of FIGS. 1A and 1B, the mirrors 90a, 90b, 92a, and 92b are used to divert the light path from the sample when measuring the reference signal (FIG. 1A). As a result, the light exiting the two paths is in general affected not only by the presence or absence of the sample, but also by the reflectance and/or transmittance of the optical elements used in the optical trains. As a result, the ratio of the reference and sample measurement signals is not simply equal to the sample transmittance as desired: in fact, the ratio may also contain other factors such as, for example, i) the reflectivity ratios of the mirrors being used in states A and B, and ii) geometrical optical effects on the signal outputs in states A and B, due to the different shape of the two beams or the different distance that the beams travel in states A and B.
The sample measurement signal produced by the light detector 14 can be expressed as follows:S1=ILSRτ1τS  (2)and the reference measurement signal produced by the light detector 14 can be expressed as follows:S0=ILSRτ0τR  (3)
where ILS is the light intensity output of the light source 12, τ1 is the optical throughput of the optical elements used in the sample measurement state (i.e., state A), τ0 is the optical throughput of the optical elements used in the reference measurement state (i.e., state B), τS is the optical throughput of the fluid sample, τR is the optical throughput of the reference material, and R is the response of the light detector 14. Defining the quantity ρm as the ratio of the signals in equations (2) and (3) above, i.e., S1/S0, the ratio ρm can be expressed as follows:
                              ρ          m                =                              τ            s                    ⁢                                    τ              1                                                      τ                R                            ⁢                              τ                0                                                                        (        4        )            
If the ratio τ1/τ0 is known and if the reference material transmission τR is known, the desired unknown quantity, τs, which contains the concentration c information, can be obtained by inverting equation (4). In principle, the quantities τ1 and τ0 can be measured to achieve this end. However, besides the fact that such measurements are cumbersome and impractical, as well as expensive due to the requirement for additional optical switching components, any changes that occur over time to the optical elements used in one optical path but not the other (e.g., the switching mirrors used in state A but not in state B) will cause errors in the concentration measurement. An example of such a change may be a change in the reflectivity of one or more of the mirrors 90a, 90b, 92a, and 92b due to aging or accumulation of dust or other particles on the reflective mirror surfaces. Current practice cannot easily compensate for such temporal changes of optical components when implementing such optical switching mechanisms. Compensation for measurement system changes can only be done using specialized separate calibration procedures to characterize the measurement system itself. Such calibration procedures typically require a shutdown or temporary removal of the measurement system from the production line to perform the calibration, which degrades the efficiency of the concentration measurements. For simplicity, the treatment above does not take into account variations in f-number or differences in travelled distance, that may also be present, and therefore may also negatively affect the final result.